Theorem simp3i 1140

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1137	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1088

This theorem is referenced by:  hartogslem2  9302  harwdom  9350  divalglem6  16107  structfn  16857  strleun  16858  oppchomfval  17423  sratset  20452  srads  20455  tngip  23809  dfrelog  25721  log2ub  26099  birthdaylem3  26103  birthday  26104  divsqrtsum2  26132  harmonicbnd2  26154  lgslem4  26448  lgscllem  26452  lgsdir2lem2  26474  lgsdir2lem3  26475  mulog2sumlem1  26682  siilem2  29214  h2hva  29336  h2hsm  29337  h2hnm  29338  elunop2  30375  wallispilem3  43608  wallispilem4  43609  prstchomval  46355